Has Earth been detected? – Another try

Yesterday I posted a modification of the Drake equation that was intended as a speculative tool – no, rather a speculative toy – to assess the probability that Earth and its biosphere have been detected by at least one alien civilization during the last three billion years. I presented an example according to which there was a 99 percent chance that our planet has been detected.

Let’s now take another try with the equation: If we change just the value of the fraction of extraterrestrial civilizations which conduct exoplanet searches (f_s in the equation) from 0.1 to 0.01, the probability that our planet has been detected lowers from 99 to 35 percent. If we further lower the average number of habitable planets per star that has planets (n_e) from 2 to 0.5 and the fraction of life-harbouring planets on which intelligence evolves (f_i) from 0.01 to 0.001, the probability of detection swings to 1 percent. So according to this example it is virtually certain that Earth has not been noticed.

The point is that both this and the Drake equation are speculative – they can be nice toys to play around with and maybe sometimes even good tools to clear up muddy thinking, but they offer no firm answers to anything.

Has Earth been detected?

Given that in the last ten years we have found roughly 250 planets outside our solar system, it is perhaps prudent to ask whether an alien civilization may have already detected our own planet and its biosphere during the approximately three billion years it has harboured photosynthesising life.

The Drake equation, the famous speculative tool to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact, was not intended to address this question but can be modified to do so. Unfortunately (but perhaps not surprisingly) this exercise necessarily involves some mathematical notation, but bear with me – it is relatively simple and in the end you will have a tool to answer (or rather, speculate) this question yourself.

The Drake equation reads:

N = R* × f_p × n_e × f_l × f_i × f_c × L

where N is the number of extraterrestrial civilizations which we might be able to contact, R* is the number of stars forming in the galaxy per year, f_p the fraction of those stars that have planets, n_e the average number of habitable planets per star that has planets, f_l the fraction of habitable planets on which life emerges, f_i the fraction of life-harbouring planets on which intelligence evolves, f_c the fraction of civilizations that start to emit detectable signals into space, and L the average number of years such civilizations continue to emit signals into space.

Drake and his colleagues originally came up with N = 10. With different assumptions we can end up with vastly varying N values, ranging for example from 0.0000001 to 5000 (see examples here). But N is the estimated number of civilizations in the Milky Way which we might be able to contact, not the probability that the Earth and its biosphere have been detected by an extraterrestrial civilization sometime during the last three billion years. For that, we need to change the equation a bit.

Given a maximum detection distance from us, for each star within that distance there is a possibility that an alien civilization residing in that system has found Earth. That possibility can be quantified as probability:

p = f_p × n_e × f_l × f_i × f_s × f_d

where f_p, n_e, f_l and f_i are the same as in the Drake equation, f_s is the fraction of civilizations that conduct exoplanet searches and f_d is the fraction of Earth-like planets actually detected in those searches. This equation assumes that life and intelligence emerged always within the last three billion years, excluding the possibility of emergence and extinction before photosynthesising life appeared on Earth.

Given the probability of single detection above, we can formulate the probability that Earth has not been detected for a given number of stars S within the maximum detection distance:

p₀ = (1 – p)^S

Now let’s plug in some numbers. I assume that alien civilizations are interested in and capable of detecting Earth-like planets within 100 light-years from they home stars. According to the Gliese Catalogue of Nearby Stars, 3rd Edition, there are 1064 stars within 50 light-years from our solar system (although it is a conservative estimate because not all stars have been catalogued). After a bit of calculation using the volume equation of a sphere and assuming constant density of stars, we end up with 8512 stars within 100 light-years from us. This will be the value of S. For f_s and f_d we assign values 0.1 and 0.5, respectively, and for the rest of the variables we use the original values of Drake and his colleagues (f_p = 0.5, n_e = 2, f_l = 1, f_i = 0.01).

So, what is the probability that Earth has not been detected? It is 0.01, so the probability that Earth has been detected by an alien civilization is 0.99 or 99 percent. Now go speculate.

Phoenix Mars Lander launches successfully

Phoenix, the NASA’s latest robotic mission to Mars, lifted off successfully from Cape Canaveral Air Force Station in Florida aboard a Delta II rocket today. After landing on Mars in May 2008 the mission will study the history of water and habitability potential in the Martian arctic’s ice-rich soil.

Harry Potter and children’s injury prevention

The launch of the last Harry Potter book – Harry Potter and the Deathly Hallows – can be seen as both good and bad news for children’s health. In December 2005 researchers from John Radcliffe Hospital, Oxford, UK, reported in British Medical Journal that they

observed a significant fall in the numbers of attendees to the emergency department on the weekends that of the two most recent Harry Potter books were released. Both these weekends were in mid-summer with good weather. It may therefore be hypothesised that there is a place for a committee of safety conscious, talented writers who could produce high quality books for the purpose of injury prevention.

So now, when there has been a new book lauch, we can expect a drop in children’s traumatic injuries – but on the other hand it was the final book.

We seem to have an urgent need for another J. K. Rowling.

🙂

Number of known extrasolar planets rising

This is a record year for exoplanet research. So far, the statistics of exoplanet.eu show that there has been already 36 new exoplanet candidates either announced in refereed papers and scientific conferences or included in papers submitted to scientific journals (see figure below).

The figure shows only the exoplanet candidates detected by the radial velocity method. By the end of the year or early next year the COROT space telescope mission is expected to start to report new candidates based on the transit method. The mission has already reported its first gas giant (but only in a press release, hence it is not included in the statistics above).